A tracial characterization of Furstenberg's xp, xq conjecture

被引：0

作者：

Bruce, Chris ^{[1
]}

Scarparo, Eduardo ^{[2
]}

机构：

[1] Univ Glasgow, Sch Math & Stat, Univ Pl, Glasgow G128QQ, Scotland

[2] Univ Fed Pelotas, Ctr Engn, Pelotas, Brazil

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2024年 / 67卷 / 01期

关键词：

Furstenberg conjecture; tracial states; primitive ideals; K-theory; C-ASTERISK-ALGEBRAS; MULTI-INVARIANT SETS; STATES;

D O I：

10.4153/S0008439523000693

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate almost minimal actions of abelian groups and their crossed products. As an application, given multiplicatively independent integers p and q, we show that Furstenberg's xp, xq conjecture holds if and only if the canonical trace is the only faithful extreme tracial state on the C*-algebra of the group Z[1/pq] (sic) Z(2). We also compute the primitive ideal space and K-theory of C*( Z[1/pq] (sic) Z(2)).

引用

页码：244 / 256

页数：13

共 50 条

[31] A variant of Shelah's characterization of Strong Chang's Conjecture
Cox, Sean
Sakai, Hiroshi
MATHEMATICAL LOGIC QUARTERLY, 2019, 65 (02) : 251 - 257
[32] Polynomials with dense zero sets and discrete models of the Kakeya conjecture and the Furstenberg set problem
Zhang, Ruixiang
SELECTA MATHEMATICA-NEW SERIES, 2017, 23 (01): : 275 - 292
[33] PHASE TRANSITIONS ON C*-ALGEBRAS ARISING FROM NUMBER FIELDS AND THE GENERALIZED FURSTENBERG CONJECTURE
Laca, Marcelo
Warren, Jacqueline M.
JOURNAL OF OPERATOR THEORY, 2020, 83 (01) : 73 - 93
[34] Identification of microduplications at Xp21.2 and Xq13.1 in neurodevelopmental disorders
Kokkonen, Hannaleena
Siren, Auli
Maatta, Tuomo
Kamila Kadlubowska, Magda
Acharya, Anushree
Nouel-Saied, Liz M.
Leal, Suzanne M.
Jarvela, Irma
Schrauwen, Isabelle
MOLECULAR GENETICS & GENOMIC MEDICINE, 2021, 9 (12):
[35] REAPPRAISAL OF A 46,X,I(XP) KARYOTYPE AS 46,X,DEL(XQ)
DELACHAPELLE, A
SCHRODER, J
HEREDITAS, 1975, 80 (01) : 137 - 140
[36] Generalizations of Furstenberg's Diophantine result
Katz, Asaf
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2018, 38 : 1012 - 1024
[37] THE SIMILARITY OF PHENOTYPIC EFFECTS CAUSED BY XP AND XQ DELETIONS IN THE HUMAN FEMALE - A HYPOTHESIS
THERMAN, E
SUSMAN, B
HUMAN GENETICS, 1990, 85 (02) : 175 - 183
[38] A note on Furstenberg's filtering problem
Garbit, Rodolphe
ISRAEL JOURNAL OF MATHEMATICS, 2011, 182 (01) : 333 - 336
[39] A note on Furstenberg’s filtering problem
Rodolphe Garbit
Israel Journal of Mathematics, 2011, 182 : 333 - 336
[40] AN IMPROVEMENT ON FURSTENBERG'S INTERSECTION PROBLEM
Yu, Han
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2021, 374 (09) : 6583 - 6610

← 1 2 3 4 5 →